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N-soliton solutions and nonlinear dynamics for two generalized Broer–Kaup systems

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Abstract

Under consideration in this paper are two nonlinear evolution models: One is the (1 + 1)-dimensional generalized Broer–Kaup (gBK) system derived by Zhang et al. (Appl Math Comput 219:5837–5848, 2013), and the other is the (2 + 1)-dimensional gBK system reported for the first time. Based on the bilinear forms given in this paper, novel N-soliton solutions of these two gBK systems are obtained by using Hirota’s bilinear method. As a comparison, the obtained two-soliton solutions of the (1 + 1)-dimensional gBK system are taken to demonstrate the difference from the known ones constructed by Darboux transformation. In order to understand the nonlinear dynamics localized in the gBK systems, local structures of the obtained one-, two-, three- and four-soliton solutions are shown. This paper reveals that each pair of the obtained N-soliton solutions of the gBK systems couple bell and kink soliton dynamics.

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Data availability statement

The authors declare that all data supporting the findings of this study are available within the article.

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Acknowledgements

The authors express their sincerest thanks to the anonymous referees for the helpful comments. This work was supported by Liaoning BaiQianWan Talents Program of China (2019 year), the Natural Science Foundation of Education Department of Liaoning Province of China (LJ2020002) and the National Science Foundation of China (11547005).

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  1. School of Mathematical Sciences, Bohai University, Jinzhou, 121013, People’s Republic of China

    Sheng Zhang & Xiaowei Zheng

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  1. Sheng Zhang
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Correspondence to Sheng Zhang.

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Zhang, S., Zheng, X. N-soliton solutions and nonlinear dynamics for two generalized Broer–Kaup systems. Nonlinear Dyn 107, 1179–1193 (2022). https://doi.org/10.1007/s11071-021-07030-w

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